(7x+5)(8x-8)=180

Solution for (7x+5)(8x-8)=180 equation:

(7x+5)(8x-8)=180

We move all terms to the left:

(7x+5)(8x-8)-(180)=0

We multiply parentheses ..

(+56x^2-56x+40x-40)-180=0

We get rid of parentheses

56x^2-56x+40x-40-180=0

We add all the numbers together, and all the variables

56x^2-16x-220=0

a = 56; b = -16; c = -220;
Δ = b2-4ac
Δ = -162-4·56·(-220)
Δ = 49536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{49536}=\sqrt{576*86}=\sqrt{576}*\sqrt{86}=24\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-24\sqrt{86}}{2*56}=\frac{16-24\sqrt{86}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+24\sqrt{86}}{2*56}=\frac{16+24\sqrt{86}}{112}
$